Convergence Rates for Gaussian Mixtures of Experts

Nhat Ho; Chiao-Yu Yang; Michael I. Jordan

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arXiv · 1907.04377

Convergence Rates for Gaussian Mixtures of Experts

Nhat Ho·Chiao-Yu Yang·Michael I. Jordan

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Abstract

We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is based on a novel notion of \emph{algebraic independence} of the expert functions. Drawing on optimal transport theory, we establish a connection between the algebraic independence and a certain class of partial differential equations (PDEs). Exploiting this connection allows us to derive convergence rates and minimax lower bounds for parameter estimation.

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BibTeX RIS

Nhat Ho, Chiao-Yu Yang, Michael I. Jordan. 2019-07-09. Convergence Rates for Gaussian Mixtures of Experts. https://arxiv.org/abs/1907.04377

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